We have measured the response of chromium-doped alumina screens to soft x-ray radiation and derived quantum efficiency curves for the energy range from 2.5 keV to 4.5 keV. Persistent luminescence (or afterglow) from this material is observed for several minutes following the removal of the x-ray source. It is also observed that the luminescence output rises gradually for several minutes before maximizing during x-ray irradiation. In the paper we discuss possible sources of this delayed luminescence and its consequences for application of these screens as soft x-ray detectors. Such screens have found application as narrow-band radiation detectors for a hot fusion plasma diagnostic.